Hyundai Xteer is more than reliable and one of its kind as its API SN, I guarantee you. Exact price of Hyundai Xteer 20W50 4L is PKR 2,120. If he is offering you a 4L pack + oil filter in 2,000, then go for it. Otherwise if he is offering you 3L + filter, I would recommend you to buy a 4L Pack at 2,120 + Oil filter which will cost you not more than 200. The reason behind recommending you to buy a 4L pack is that you already said your piston rings are weak. Go for 4L so that you may top up the engine oil if leaked inside engine.
Moreover, I would say that don't always believe in mechanics, if I was having a car like yours, I would go for engine flush first. There are several type of engine flush available in market. My recommendation would be Liqui Moly engine flush. Pour it in the engine oil compartment before oil change, start the engine idle and let it there for "minutes" directed on the pack of liqui moly engine flush. after this, flush all the oil from engine, ask the oil change wala to blow some air in engine oil compartment for maximum extraction of engine oil. Pour your Hyundai Xteer GSL 20W50 along with new oil filter. Here I would recommend you to please change the air filter as well. Start the engine, check any leakage. I must tell you in ideal conditions, Hyundai Xteer is able to work for almost 12-15,000 kms.